In one word dont.
Either you will have a garden or you wont.
Puppies, dogs and gardens, especially a young dog dont mix.
Fence it of, star pickets and makethe wire about 12 inches deep with
chook wire, and a gate.
Also expect some entries into the garden when you forget the gate.
And dont even think of a labrador (grin!)

Staycalm wrote:
I have a lovely established veggie garden in the back yard. I am planning to
get a puppy or young dog (small breed) in the next 4 months or so.
Should I plan to fence off the veggie garden in some way?
What can I use that's not too costly but will protect the patch?
Liz